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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #include "Acts/Surfaces/CylinderSurface.hpp"
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Definitions/Tolerance.hpp"
 #include "Acts/Definitions/Units.hpp"
 #include "Acts/Geometry/GeometryObject.hpp"
 #include "Acts/Surfaces/CylinderBounds.hpp"
 #include "Acts/Surfaces/SurfaceError.hpp"
 #include "Acts/Surfaces/SurfaceMergingException.hpp"
 #include "Acts/Surfaces/detail/AlignmentHelper.hpp"
 #include "Acts/Surfaces/detail/FacesHelper.hpp"
 #include "Acts/Surfaces/detail/MergeHelper.hpp"
 #include "Acts/Utilities/Intersection.hpp"
 #include "Acts/Utilities/ThrowAssert.hpp"
 #include "Acts/Utilities/detail/periodic.hpp"
 
 #include <algorithm>
 #include <cassert>
 #include <cmath>
 #include <iostream>
 #include <memory>
 #include <stdexcept>
 #include <utility>
 #include <vector>
 
 namespace Acts {
 
 using VectorHelpers::perp;
 using VectorHelpers::phi;
 
 CylinderSurface::CylinderSurface(const CylinderSurface& other)
     : GeometryObject(), RegularSurface(other), m_bounds(other.m_bounds) {}
 
 CylinderSurface::CylinderSurface(const GeometryContext& gctx,
                                  const CylinderSurface& other,
                                  const Transform3& shift)
     : GeometryObject(),
       RegularSurface(gctx, other, shift),
       m_bounds(other.m_bounds) {}
 
 CylinderSurface::CylinderSurface(const Transform3& transform, double radius,
                                  double halfz, double halfphi, double avphi,
                                  double bevelMinZ, double bevelMaxZ)
     : RegularSurface(transform),
       m_bounds(std::make_shared<const CylinderBounds>(
           radius, halfz, halfphi, avphi, bevelMinZ, bevelMaxZ)) {}
 
 CylinderSurface::CylinderSurface(std::shared_ptr<const CylinderBounds> cbounds,
                                  const DetectorElementBase& detelement)
     : RegularSurface(detelement), m_bounds(std::move(cbounds)) {
   // surfaces representing a detector element must have bounds
   throw_assert(m_bounds, "CylinderBounds must not be nullptr");
 }
 
 CylinderSurface::CylinderSurface(const Transform3& transform,
                                  std::shared_ptr<const CylinderBounds> cbounds)
     : RegularSurface(transform), m_bounds(std::move(cbounds)) {
   throw_assert(m_bounds, "CylinderBounds must not be nullptr");
 }
 
 CylinderSurface& CylinderSurface::operator=(const CylinderSurface& other) {
   if (this != &other) {
     Surface::operator=(other);
     m_bounds = other.m_bounds;
   }
   return *this;
 }
 
 // return the binning position for ordering in the BinnedArray
 Vector3 CylinderSurface::referencePosition(const GeometryContext& gctx,
                                            AxisDirection aDir) const {
   // special binning type for R-type methods
   if (aDir == AxisDirection::AxisR || aDir == AxisDirection::AxisRPhi) {
     double R = bounds().get(CylinderBounds::eR);
     double phi = bounds().get(CylinderBounds::eAveragePhi);
     return localToGlobal(gctx, Vector2{phi * R, 0});
   }
   // give the center as default for all of these binning types
   // AxisDirection::AxisX, AxisDirection::AxisY, AxisDirection::AxisZ,
   // AxisDirection::AxisR, AxisDirection::AxisPhi, AxisDirection::AxisRPhi,
   // AxisDirection::AxisTheta, AxisDirection::AxisEta
   return center(gctx);
 }
 
 // return the measurement frame: it's the tangential plane
 RotationMatrix3 CylinderSurface::referenceFrame(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& /*direction*/) const {
   RotationMatrix3 mFrame;
   // construct the measurement frame
   // measured Y is the z axis
   Vector3 measY = rotSymmetryAxis(gctx);
   // measured z is the position normalized transverse (in local)
   Vector3 measDepth = normal(gctx, position);
   // measured X is what comoes out of it
   Vector3 measX(measY.cross(measDepth).normalized());
   // assign the columnes
   mFrame.col(0) = measX;
   mFrame.col(1) = measY;
   mFrame.col(2) = measDepth;
   // return the rotation matrix
   return mFrame;
 }
 
 Surface::SurfaceType CylinderSurface::type() const {
   return Surface::Cylinder;
 }
 
 Vector3 CylinderSurface::localToGlobal(const GeometryContext& gctx,
                                        const Vector2& lposition) const {
   // create the position in the local 3d frame
   double r = bounds().get(CylinderBounds::eR);
   double phi = lposition[0] / r;
   Vector3 position(r * cos(phi), r * sin(phi), lposition[1]);
   return transform(gctx) * position;
 }
 
 Result<Vector2> CylinderSurface::globalToLocal(const GeometryContext& gctx,
                                                const Vector3& position,
                                                double tolerance) const {
   double inttol = tolerance;
   if (tolerance == s_onSurfaceTolerance) {
     // transform default value!
     // @TODO: check if s_onSurfaceTolerance would do here
     inttol = bounds().get(CylinderBounds::eR) * 0.0001;
   }
   if (inttol < 0.01) {
     inttol = 0.01;
   }
   const Transform3& sfTransform = transform(gctx);
   Transform3 inverseTrans(sfTransform.inverse());
   Vector3 loc3Dframe(inverseTrans * position);
   if (std::abs(perp(loc3Dframe) - bounds().get(CylinderBounds::eR)) > inttol) {
     return Result<Vector2>::failure(SurfaceError::GlobalPositionNotOnSurface);
   }
   return Result<Vector2>::success(
       {bounds().get(CylinderBounds::eR) * phi(loc3Dframe), loc3Dframe.z()});
 }
 
 std::string CylinderSurface::name() const {
   return "Acts::CylinderSurface";
 }
 
 Vector3 CylinderSurface::normal(const GeometryContext& gctx,
                                 const Vector2& lposition) const {
   double phi = lposition[0] / m_bounds->get(CylinderBounds::eR);
   Vector3 localNormal(cos(phi), sin(phi), 0.);
   return transform(gctx).linear() * localNormal;
 }
 
 Vector3 CylinderSurface::normal(const GeometryContext& gctx,
                                 const Vector3& position) const {
   const Transform3& sfTransform = transform(gctx);
   // get it into the cylinder frame
   Vector3 pos3D = sfTransform.inverse() * position;
   // set the z coordinate to 0
   pos3D.z() = 0.;
   // normalize and rotate back into global
   return sfTransform.linear() * pos3D.normalized();
 }
 
 double CylinderSurface::pathCorrection(const GeometryContext& gctx,
                                        const Vector3& position,
                                        const Vector3& direction) const {
   Vector3 normalT = normal(gctx, position);
   double cosAlpha = normalT.dot(direction);
   return std::abs(1. / cosAlpha);
 }
 
 const CylinderBounds& CylinderSurface::bounds() const {
   return *m_bounds;
 }
 
 Polyhedron CylinderSurface::polyhedronRepresentation(
     const GeometryContext& gctx, unsigned int quarterSegments) const {
   auto ctrans = transform(gctx);
 
   // Prepare vertices and faces
   std::vector<Vector3> vertices =
       bounds().circleVertices(ctrans, quarterSegments);
   auto [faces, triangularMesh] =
       detail::FacesHelper::cylindricalFaceMesh(vertices);
   return Polyhedron(vertices, faces, triangularMesh, false);
 }
 
 Vector3 CylinderSurface::rotSymmetryAxis(const GeometryContext& gctx) const {
   // fast access via transform matrix (and not rotation())
   return transform(gctx).matrix().block<3, 1>(0, 2);
 }
 
 detail::RealQuadraticEquation CylinderSurface::intersectionSolver(
     const Transform3& transform, const Vector3& position,
     const Vector3& direction) const {
   // Solve for radius R
   double R = bounds().get(CylinderBounds::eR);
 
   // Get the transformation matrtix
   const auto& tMatrix = transform.matrix();
   Vector3 caxis = tMatrix.block<3, 1>(0, 2).transpose();
   Vector3 ccenter = tMatrix.block<3, 1>(0, 3).transpose();
 
   // Check documentation for explanation
   Vector3 pc = position - ccenter;
   Vector3 pcXcd = pc.cross(caxis);
   Vector3 ldXcd = direction.cross(caxis);
   double a = ldXcd.dot(ldXcd);
   double b = 2. * (ldXcd.dot(pcXcd));
   double c = pcXcd.dot(pcXcd) - (R * R);
   // And solve the qaudratic equation
   return detail::RealQuadraticEquation(a, b, c);
 }
 
 MultiIntersection3D CylinderSurface::intersect(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& direction, const BoundaryTolerance& boundaryTolerance,
     double tolerance) const {
   const auto& gctxTransform = transform(gctx);
 
   // Solve the quadratic equation
   auto qe = intersectionSolver(gctxTransform, position, direction);
 
   // If no valid solution return a non-valid surfaceIntersection
   if (qe.solutions == 0) {
     return MultiIntersection3D(Intersection3D::Invalid(),
                                Intersection3D::Invalid());
   }
 
   // Check the validity of the first solution
   Vector3 solution1 = position + qe.first * direction;
   IntersectionStatus status1 = std::abs(qe.first) < std::abs(tolerance)
                                    ? IntersectionStatus::onSurface
                                    : IntersectionStatus::reachable;
 
   // Helper method for boundary check
   auto boundaryCheck = [&](const Vector3& solution,
                            IntersectionStatus status) -> IntersectionStatus {
     // No check to be done, return current status
     if (boundaryTolerance.isInfinite()) {
       return status;
     }
     if (boundaryTolerance.isNone() && bounds().coversFullAzimuth()) {
       // Project out the current Z value via local z axis
       // Built-in local to global for speed reasons
       const auto& tMatrix = gctxTransform.matrix();
       // Create the reference vector in local
       const Vector3 vecLocal(solution - tMatrix.block<3, 1>(0, 3));
       double cZ = vecLocal.dot(tMatrix.block<3, 1>(0, 2));
       double hZ = bounds().get(CylinderBounds::eHalfLengthZ) + tolerance;
       return std::abs(cZ) < std::abs(hZ) ? status
                                          : IntersectionStatus::unreachable;
     }
     return isOnSurface(gctx, solution, direction, boundaryTolerance)
                ? status
                : IntersectionStatus::unreachable;
   };
   // Check first solution for boundary compatibility
   status1 = boundaryCheck(solution1, status1);
   // Set the intersection
   Intersection3D first(solution1, qe.first, status1);
   if (qe.solutions == 1) {
     return MultiIntersection3D(first, first);
   }
   // Check the validity of the second solution
   Vector3 solution2 = position + qe.second * direction;
   IntersectionStatus status2 = std::abs(qe.second) < std::abs(tolerance)
                                    ? IntersectionStatus::onSurface
                                    : IntersectionStatus::reachable;
   // Check first solution for boundary compatibility
   status2 = boundaryCheck(solution2, status2);
   Intersection3D second(solution2, qe.second, status2);
   // Order based on path length
   if (first.pathLength() <= second.pathLength()) {
     return MultiIntersection3D(first, second);
   }
   return MultiIntersection3D(second, first);
 }
 
 AlignmentToPathMatrix CylinderSurface::alignmentToPathDerivative(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& direction) const {
   assert(isOnSurface(gctx, position, direction, BoundaryTolerance::Infinite()));
 
   // The vector between position and center
   const auto pcRowVec = (position - center(gctx)).transpose().eval();
   // The rotation
   const auto& rotation = transform(gctx).rotation();
   // The local frame x/y/z axis
   const auto& localXAxis = rotation.col(0);
   const auto& localYAxis = rotation.col(1);
   const auto& localZAxis = rotation.col(2);
   // The local coordinates
   const auto localPos = (rotation.transpose() * position).eval();
   const auto dx = direction.dot(localXAxis);
   const auto dy = direction.dot(localYAxis);
   const auto dz = direction.dot(localZAxis);
   // The normalization factor
   const auto norm = 1 / (1 - dz * dz);
   // The direction transpose
   const auto& dirRowVec = direction.transpose();
   // The derivative of path w.r.t. the local axes
   // @note The following calculations assume that the intersection of the track
   // with the cylinder always satisfy: perp(localPos) = R
   const auto localXAxisToPath =
       (-2 * norm * (dx * pcRowVec + localPos.x() * dirRowVec)).eval();
   const auto localYAxisToPath =
       (-2 * norm * (dy * pcRowVec + localPos.y() * dirRowVec)).eval();
   const auto localZAxisToPath =
       (-4 * norm * norm * (dx * localPos.x() + dy * localPos.y()) * dz *
        dirRowVec)
           .eval();
   // Calculate the derivative of local frame axes w.r.t its rotation
   const auto [rotToLocalXAxis, rotToLocalYAxis, rotToLocalZAxis] =
       detail::rotationToLocalAxesDerivative(rotation);
   // Initialize the derivative of propagation path w.r.t. local frame
   // translation (origin) and rotation
   AlignmentToPathMatrix alignToPath = AlignmentToPathMatrix::Zero();
   alignToPath.segment<3>(eAlignmentCenter0) =
       2 * norm * (dx * localXAxis.transpose() + dy * localYAxis.transpose());
   alignToPath.segment<3>(eAlignmentRotation0) =
       localXAxisToPath * rotToLocalXAxis + localYAxisToPath * rotToLocalYAxis +
       localZAxisToPath * rotToLocalZAxis;
 
   return alignToPath;
 }
 
 ActsMatrix<2, 3> CylinderSurface::localCartesianToBoundLocalDerivative(
     const GeometryContext& gctx, const Vector3& position) const {
   using VectorHelpers::perp;
   using VectorHelpers::phi;
   // The local frame transform
   const auto& sTransform = transform(gctx);
   // calculate the transformation to local coordinates
   const Vector3 localPos = sTransform.inverse() * position;
   const double lr = perp(localPos);
   const double lphi = phi(localPos);
   const double lcphi = std::cos(lphi);
   const double lsphi = std::sin(lphi);
   // Solve for radius R
   double R = bounds().get(CylinderBounds::eR);
   ActsMatrix<2, 3> loc3DToLocBound = ActsMatrix<2, 3>::Zero();
   loc3DToLocBound << -R * lsphi / lr, R * lcphi / lr, 0, 0, 0, 1;
 
   return loc3DToLocBound;
 }
 
 std::pair<std::shared_ptr<CylinderSurface>, bool> CylinderSurface::mergedWith(
     const CylinderSurface& other, AxisDirection direction,
     bool externalRotation, const Logger& logger) const {
   using namespace UnitLiterals;
 
   ACTS_VERBOSE("Merging cylinder surfaces in " << axisDirectionName(direction)
                                                << " direction");
 
   if (m_associatedDetElement != nullptr ||
       other.m_associatedDetElement != nullptr) {
     throw SurfaceMergingException(getSharedPtr(), other.getSharedPtr(),
                                   "CylinderSurface::merge: surfaces are "
                                   "associated with a detector element");
   }
 
   assert(m_transform != nullptr && other.m_transform != nullptr);
 
   Transform3 otherLocal = m_transform->inverse() * *other.m_transform;
 
   constexpr auto tolerance = s_onSurfaceTolerance;
 
   // surface cannot have any relative rotation
 
   if (std::abs(otherLocal.linear().col(eX)[eZ]) >= tolerance ||
       std::abs(otherLocal.linear().col(eY)[eZ]) >= tolerance) {
     ACTS_ERROR("CylinderSurface::merge: surfaces have relative rotation");
     throw SurfaceMergingException(
         getSharedPtr(), other.getSharedPtr(),
         "CylinderSurface::merge: surfaces have relative rotation");
   }
 
   auto checkNoBevel = [this, &logger, &other](const auto& bounds) {
     if (bounds.get(CylinderBounds::eBevelMinZ) != 0.0) {
       ACTS_ERROR(
           "CylinderVolumeStack requires all volumes to have a bevel angle of "
           "0");
       throw SurfaceMergingException(
           getSharedPtr(), other.getSharedPtr(),
           "CylinderVolumeStack requires all volumes to have a bevel angle of "
           "0");
     }
 
     if (bounds.get(CylinderBounds::eBevelMaxZ) != 0.0) {
       ACTS_ERROR(
           "CylinderVolumeStack requires all volumes to have a bevel angle of "
           "0");
       throw SurfaceMergingException(
           getSharedPtr(), other.getSharedPtr(),
           "CylinderVolumeStack requires all volumes to have a bevel angle of "
           "0");
     }
   };
 
   checkNoBevel(bounds());
   checkNoBevel(other.bounds());
 
   // radii need to be identical
   if (std::abs(bounds().get(CylinderBounds::eR) -
                other.bounds().get(CylinderBounds::eR)) > tolerance) {
     ACTS_ERROR("CylinderSurface::merge: surfaces have different radii");
     throw SurfaceMergingException(
         getSharedPtr(), other.getSharedPtr(),
         "CylinderSurface::merge: surfaces have different radii");
   }
 
   double r = bounds().get(CylinderBounds::eR);
 
   // no translation in x/z is allowed
   Vector3 translation = otherLocal.translation();
 
   if (std::abs(translation[0]) > tolerance ||
       std::abs(translation[1]) > tolerance) {
     ACTS_ERROR(
         "CylinderSurface::merge: surfaces have relative translation in x/y");
     throw SurfaceMergingException(
         getSharedPtr(), other.getSharedPtr(),
         "CylinderSurface::merge: surfaces have relative translation in x/y");
   }
 
   double hlZ = bounds().get(CylinderBounds::eHalfLengthZ);
   double minZ = -hlZ;
   double maxZ = hlZ;
 
   double zShift = translation[2];
   double otherHlZ = other.bounds().get(CylinderBounds::eHalfLengthZ);
   double otherMinZ = -otherHlZ + zShift;
   double otherMaxZ = otherHlZ + zShift;
 
   double hlPhi = bounds().get(CylinderBounds::eHalfPhiSector);
   double avgPhi = bounds().get(CylinderBounds::eAveragePhi);
 
   double otherHlPhi = other.bounds().get(CylinderBounds::eHalfPhiSector);
   double otherAvgPhi = other.bounds().get(CylinderBounds::eAveragePhi);
 
   if (direction == AxisDirection::AxisZ) {
     // z shift must match the bounds
 
     if (std::abs(otherLocal.linear().col(eY)[eX]) >= tolerance &&
         (!bounds().coversFullAzimuth() ||
          !other.bounds().coversFullAzimuth())) {
       throw SurfaceMergingException(getSharedPtr(), other.getSharedPtr(),
                                     "CylinderSurface::merge: surfaces have "
                                     "relative rotation in z and phi sector");
     }
 
     ACTS_VERBOSE("this: [" << minZ << ", " << maxZ << "] ~> "
                            << (minZ + maxZ) / 2.0 << " +- " << hlZ);
     ACTS_VERBOSE("zShift: " << zShift);
 
     ACTS_VERBOSE("other: [" << otherMinZ << ", " << otherMaxZ << "] ~> "
                             << (otherMinZ + otherMaxZ) / 2.0 << " +- "
                             << otherHlZ);
     if (std::abs(maxZ - otherMinZ) > tolerance &&
         std::abs(minZ - otherMaxZ) > tolerance) {
       ACTS_ERROR("CylinderSurface::merge: surfaces have incompatible z bounds");
       throw SurfaceMergingException(
           getSharedPtr(), other.getSharedPtr(),
           "CylinderSurface::merge: surfaces have incompatible z bounds");
     }
 
     if (hlPhi != otherHlPhi || avgPhi != otherAvgPhi) {
       throw SurfaceMergingException(getSharedPtr(), other.getSharedPtr(),
                                     "CylinderSurface::merge: surfaces have "
                                     "different phi sectors");
     }
 
     double newMaxZ = std::max(maxZ, otherMaxZ);
     double newMinZ = std::min(minZ, otherMinZ);
     double newHlZ = (newMaxZ - newMinZ) / 2.0;
     double newMidZ = (newMaxZ + newMinZ) / 2.0;
     ACTS_VERBOSE("merged: [" << newMinZ << ", " << newMaxZ << "] ~> " << newMidZ
                              << " +- " << newHlZ);
 
     auto newBounds = std::make_shared<CylinderBounds>(r, newHlZ, hlPhi, avgPhi);
 
     Transform3 newTransform =
         *m_transform * Translation3{Vector3::UnitZ() * newMidZ};
 
     return {Surface::makeShared<CylinderSurface>(newTransform, newBounds),
             zShift < 0};
 
   } else if (direction == AxisDirection::AxisRPhi) {
     // no z shift is allowed
     if (std::abs(translation[2]) > tolerance) {
       ACTS_ERROR(
           "CylinderSurface::merge: surfaces have relative translation in z for "
           "rPhi merging");
       throw SurfaceMergingException(
           getSharedPtr(), other.getSharedPtr(),
           "CylinderSurface::merge: surfaces have relative translation in z for "
           "rPhi merging");
     }
 
     if (hlZ != otherHlZ) {
       throw SurfaceMergingException(getSharedPtr(), other.getSharedPtr(),
                                     "CylinderSurface::merge: surfaces have "
                                     "different z bounds");
     }
 
     // Figure out signed relative rotation
     Vector2 rotatedX = otherLocal.linear().col(eX).head<2>();
     double zrotation = std::atan2(rotatedX[1], rotatedX[0]);
 
     ACTS_VERBOSE("this:  [" << avgPhi / 1_degree << " +- " << hlPhi / 1_degree
                             << "]");
     ACTS_VERBOSE("other: [" << otherAvgPhi / 1_degree << " +- "
                             << otherHlPhi / 1_degree << "]");
 
     ACTS_VERBOSE("Relative rotation around local z: " << zrotation / 1_degree);
 
     double prevOtherAvgPhi = otherAvgPhi;
     otherAvgPhi = detail::radian_sym(otherAvgPhi + zrotation);
     ACTS_VERBOSE("~> local other average phi: "
                  << otherAvgPhi / 1_degree
                  << " (was: " << prevOtherAvgPhi / 1_degree << ")");
 
     try {
       auto [newHlPhi, newAvgPhi, reversed] = detail::mergedPhiSector(
           hlPhi, avgPhi, otherHlPhi, otherAvgPhi, logger, tolerance);
 
       Transform3 newTransform = *m_transform;
 
       if (externalRotation) {
         ACTS_VERBOSE("Modifying transform for external rotation of "
                      << newAvgPhi / 1_degree);
         newTransform = newTransform * AngleAxis3(newAvgPhi, Vector3::UnitZ());
         newAvgPhi = 0.;
       }
 
       auto newBounds = std::make_shared<CylinderBounds>(
           r, bounds().get(CylinderBounds::eHalfLengthZ), newHlPhi, newAvgPhi);
 
       return {Surface::makeShared<CylinderSurface>(newTransform, newBounds),
               reversed};
     } catch (const std::invalid_argument& e) {
       throw SurfaceMergingException(getSharedPtr(), other.getSharedPtr(),
                                     e.what());
     }
   } else {
     throw SurfaceMergingException(getSharedPtr(), other.getSharedPtr(),
                                   "CylinderSurface::merge: invalid direction " +
                                       axisDirectionName(direction));
   }
 }
 
 }  // namespace Acts

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